Are regression weights in SEM the same thing as in say, a weight in linear regression (for each 1 more of this predictor, there's 2 more of y)? And how should you decide which weight should be fixed to 1? Does it even matter?
Regression weights in SEM are the same as regression weights in linear regression.
In R, if you run:
library(lavaan) data(attitude) summary(glm(rating ~ complaints + privileges, data = attitude)) m <- 'rating ~ complaints + privileges' summary(sem(m, attitude))
You'll find that the results of the two models are close to identical.
I don't think you should fix any weight to 1. But you should often fix a factor loading to 1. It doesn't make any difference empirically which is fixed - it rescales the loadings. Sometimes it makes theoretical sense to choose one of the variables to have its loading fixed to one - this is the variable with the closest conceptual relationship to the latent variable of interest.